3. The attempt at a solution
1) According to my text the tangent line to the curve r(t) = f(t)i + g(t)j + h(t)k is the line that passes through the point (f(t0), g(t0), h(t0)) parallel to v(t0), where t0 = 0 in this problem.
I solved the velocity equation v(t) = (cos t)i + (2t + sin t)j + (e^t)k, and v(0) = i + k.
This is the answer:
x = t, y = -1, z = 1+t
I found the point (f(0), g(0), t(0)) = (0, -1, 1), I'm not sure how to find the equation of a line that passes through this point and is parallel to another line? thanks

2) For this one I just want to make sure, to find where the acceleration vector is orthogonal to its velocity vector I find where their dot products equal 0, right?